The first calculation of energy exchange between electrons and the radiation field by inverse Compton and Compton recoil was reported by Hurwitz in Los Alamos Reports LA-301 (1945) and LA-553 (1946). These reports have not been generally known; even in 1950, Bethe called attention to their neglect. Yet, they predated Kompaneets’s widely cited 1957 paper and original 1950 report. “Comptonization” is important in many astronomical objects as well as in fusion energy. I make a very brief comparison with Kompaneets’s work and present Hurwitz’s reports as appendixes.